Some results on the admissible representations of non-connected reductive p-adic groups

1995/11/09 by Goldberg, David, Herb, Rebecca A.
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/9511216

Abstract

We examine the theory of induced representations for non-connected reductive p-adic groups for which G/G0 is abelian. We first examine the structure of those representations of the form \IndP0G(σ), where P0 is a parabolic subgroup of G0 and \s is a discrete series representation of the Levi component of P0. Here we develop a theory of R--groups, extending the theory in the connected case. We then prove some general results in the theory of representations of non-connected p-adic groups whose component group is abelian. We define the notion of cuspidal parabolic for G in order to give a context for this discussion. Intertwining operators for the non-connected case are examined and the notions of supercuspidal and discrete series are defined. Finally, we examine parabolic induction from a cuspidal parabolic subgroup of G. Here we also develop a theory of R--groups, and show that these groups parameterize the induced representations in a manner that is consistent with the connected case and with the first set of results as well.

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